Dewey's Logical Theory: New Studies and Interpretations

6. Prospects for Mathematizing Dewey's Logical Theory

121 6 ProspectsforMathematizing Dewey’sLogicalTheory Tom Burke This essay discusses ways in which contemporary mathematical logic may be reconciled with John Dewey’s logical theory. Standard formal techniques drawn from dynamic modal logic, situation theory, fuzzy set theory and fuzzy logic, generative grammar, generalized quantifier theory, category theory, lambda calculi, game theoretic semantics, network exchange theory, etc., are accommodated within a framework consistent with Dewey’s Logic: The Theory of Inquiry (1938). This essay outlines many of the basic features of Dewey’s logical theory, working in a top-down fashion through various technical notions pertaining to existential and ideational aspects of inquiry, from contextual notions of situations and ideologies, to primitive operational and empirical notions of modes of action and particular qualities. The aim here is to display the scope of Dewey’s logical theory and thus establish a framework relative to which details may be explored without losing sight of their larger significance. Dewey’s Perspective on Logic [T]he insistent theme of the [1938] Logic is that an adequate system of symbolization is contingent on both a better theory of language than was then available to philosophical logicians and a better theory of the materials to be symbolized. . . . His Logic is dedicated, Dewey says in the preface, to the conviction that the general principles of language which he will set forth “will enable a more complete and consistent set of symbolizations than now exists to be made.” (Sleeper 1986/2001, 135–36) This essay takes these remarks at face value. Matters have progressed such that we may begin to propose strategies for reconciling Dewey’s philoso- 122 Tom Burke phy of logic with contemporary mathematical logic and natural language semantics—not necessarily because linguists and logicians are now working with better theories of language or better theories of the ontological commitments of mathematical logic but because more sophisticated systems of “symbolization” have been developed which more easily accommodate the kind of logical theory that Dewey presented. Dewey’s 1938 Logic casts logic as a scientific inquiry into general features of inquiry itself, with the aim of determining normative principles that distinguish better and worse methods of inquiry. Can this view of logic accommodate formal techniques and principles of contemporary mathematical logic? Specifically, how do we position such technical concerns within Dewey’s theory of inquiry? How do we link them to the operational and empirical foundations of that theory? Can this be done without compromising Dewey’s conceptions of inquiry and experience? Contemporary mathematical logic is more technically sophisticated than anything Dewey was in a position to consider in his day. But if he was right about what logic is and what inquiry is, then these technical developments should fall within the scope of his logical theory. Reconciling Dewey’s view of logic with contemporary mathematical logic will not be straightforward insofar as Dewey imposed various stringent constraints on logic as a science. In particular, to say that logical theory should be fundamentally oriented to operational and empirical concerns is not to say that it should be oriented exclusively to inductive inference. But it means that human conceptual schemes and linguistic capabilities are based ultimately on our abilities to act in the world, individually and collectively , and to note and interpret the results of those actions. Natural language semantics and issues regarding “logical form,” deductive or otherwise , would then depend on operational and empirical matters as much as they do on sentential truth-functions or a set-theoretic semantics for names, predicate symbols, variables, and quantifiers. The objects, properties, and relations in the world of things we typically observe, talk about, and have knowledge of would be products of interactions and transactions that are made possible because of our operational and empirical capabilities. If formal semantic theories are to explicitly accommodate this transactional character of experience, language, thought, and knowledge, then we have to start with a set of basic notions that are often regarded as extralogical— namely, notions of agents’ operational abilities and of their capacities to register the results of such actions. Only on that basis should we introduce notions of things, entities, objects, occasions, space-time points, events, or whatever else may belong to domains of discourse, have properties, stand in relations to one another, or otherwise characterize possible or actual Mathematizing Dewey’s Logical Theory 123 states of affairs. This requires an integrated type of operationalism and empiricism affecting every aspect...